A one-dimensional mathematical model of a spirally wound lithium/thionyl chloride primary battery is developed and used for parameter estimation and design studies. The model formulation is based on the fundamental conservation laws using porous electrode theory and concentrated solution theory. The model is used to estimate the transference number, the diffusion coefficient. and the kinetic parameters for the reactions at the anode and the cathode as a function of temperature. These parameters are obtained by fitting the simulated capacity and average cell voltage to experimental data over a wide range of temperatures (-55 to 49 degrees C) and discharge loads (10-250 Ohm). The experiments were performed on D-sized, cathode-limited, spirally wound lithium/thionyl chloride cells. The model is also used to study the effect of cathode thickness on the cell capacity as a function of temperature, and it was found that the optimum thickness for the cathode-limited design is temperature and load dependent.